Thermodynamics of black holes were studied by Hawking, Bekenstein et al., considering black holes as classical spacetimes possessing a singular region hidden behind an event horizon. In this chapter, in contrast, we treat black hole from the perspective of a generic theory of quantum gravity, using certain assumptions which are consistent with loop quantum gravity (LQG). Using these assumptions and basic tenets of equilibrium statistical mechanics, we have derived criteria for thermal stability of black holes in any spacetime dimension with arbitrary number of charges (‘hairs’), irrespective of whether classical or quantum. The derivation of these thermal stability criteria makes no explicit use of classical spacetime geometry at all. The only assumption is that the mass of the black hole is a function of its horizon area and all the ‘hairs’ (i.e. charge, angular momentum, any other types of hairs). We get a series of inequalities between derivatives of the mass function with respect to the area and other ‘hairs’ as the thermal stability criteria. These criteria are then tested in detail against various types of black holes in various dimensions. This permits us to predict the region of the parameter space of a given black hole in which it may be stable under Hawking radiation.
Part of the book: New Ideas Concerning Black Holes and the Universe
Black holes and Dark matter are two fascinating things that are known very little. They may have non gravitational interactions, but those are definitely extremely feeble in comparison to their gravitational interactions. Nowadays some people think that one may contain the other. In this chapter we will see that some black holes may contain the dark matter. These black holes decay under Hawking radiation, but do not vanish completely. They produce stable end states due to both quantum gravitational effects and thermodynamic reasons. These end states are the replicas of what we call dark matter. We will develop the complete theory for decay of such black holes, starting from some scheme independent assumptions for the quantum mechanical nature of the black holes. We will then consider explicit examples of some black holes to show that they indeed produce replicas of dark matter at their end states. Thus this chapter is going to be a manuscript for theoretical development of black hole decay from a quantum mechanical perspective and its consequences for producing replicas of dark matter.
Part of the book: Dark Matter